IB Maths SL TYPE I Lacsap’s Fractions Portfolio Lacsap’s fraction Introduction: Lacsap’s fraction is a symmetrical triangle that has the following pattern in the first five rows The shape is similar to Pascal triangle. It has the same quantity of symmetrical triangle as Pascal triangle. And Lacsap is the inverse alphabet order of Pascal. These make me think about Pascal triangle and I made an assumption that elements in Lacsap triangle may have the same relationship as in Pascal triangle
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Lacsap’s Fractions The aim if this IA is to investigate Lacsap’s Fractions and to come up with a general statement for finding the terms. When I noticed that Lacsap was Pascal spelt backwards I decided to look for a connection with Pascal’s triangle. Pascal’s triangle is used to show the numbers of ‘n’ choose ‘r’(nCr). The row number represents the value of ‘and the column number represents the ‘r’ value. Eg. Row 3‚ colomn 2 = 3C2 =
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In Lacsap’s Fractions‚ when looking for a general pattern for the numerator‚ it can be noted that it does not increase linearly but exponentially. Numerators are 3‚6‚10‚ and 15‚ each preceding numerator added by one plus the row number. Using this general statement it can be concluded that the numerator in the 6th row is 21 (15+6)‚ and 28 for the 7th. Generating a Statement for the Numerator: To generate an equation for the numerator of the fraction‚ the fraction data must be organized and
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In Lacsap’s Fractions‚ En(r) refers to the (r+1)th term in the nth row. The numerator and denominator are found separately‚ therefore to find the general statement‚ two different equations‚ one for the numerator and one for the denominator‚ must be found. Let M=numerator and let D=denominator so that En(r) = M/D. To find the numerator for any number of Lacsap’s Fractions‚ an equation must be made that uses the row number to find the numerator. Because the numerator changes depending on the row
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Lacsap’s Fractions Laurie Scott SL Math Internal Assessment Mr. Winningham 9/5/12 Instructions: In this task you will consider a set of numbers that are presented in a symmetrical pattern. Pascal’s Triangle |n=0 |1 | |1 |0 | |2 |3 | |3 |6 | |4 |10
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| Math SL Portfolio-Lacsap’s Fractions | Type 1: Investigation Portfolio Greenwood High (An International School) | | | | | Table of Contents: Introduction……………………………………………………………………………………………………..……..…...Page 2 Patterns in Numerator………………………………………………………………………………….………………Page 2 and Page 3 Plotting Graph of Row Number and Numerator……………………………………………………………Page 4 to Page 7 Finding Denominator………………………………………………….………………………………………..………Page 8 to Page 9 Finding Further Rows……………………………………………………………………
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Jonghyun Choe March 25 2011 Math IB SL Internal Assessment – LASCAP’S Fraction The goal of this task is to consider a set of fractions which are presented in a symmetrical‚ recurring sequence‚ and to find a general statement for the pattern. The presented pattern is: Row 1 1 1 Row 2 1 32 1 Row
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MATH INVESTIGATION 4.2 FACTORIZATIONS on the Math Investigator determines if a number is prime or composite. If a number is composite‚ it prints all its factors‚ the number of factors‚ and its prime factorization. The numbers 1‚ 2‚ 4‚ and 6 have 1‚ 2‚ 3‚ and 4 factors‚ respectively: 1 has only 1 as a factor; 2 has 1 and 2 as factors; 4 has 1‚ 2‚ and 4 as factors; and 6 has 1‚ 2‚ 3‚ and 6 as factors. These factors are illustrated by the rectangles shown here. Starting Points for Investigations
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Pascal’s triangle. Another hint can also easily be noticed as Lacsap is exactly the backwards of Pascal. The goal of the investigation is to find the general statement En(r)‚ where En(r) is the (r+1)th element in the nth row‚ starting with r=0. An example of this would be . In order to develop the general statement for En(r)‚ patterns have to be found for the calculation of the numerator and the denominator. Figure 1: Lacsap’s fractions 1 1 1 3/2 1 1 6/4 6/4 1 1
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References: Albrecht‚ W. S.‚ & Stack‚ R. J. (1999). Accounting education: Charting the course through a perilous future Albrecht‚ W. S.‚ & Sack‚ R. J. (2001). The perilous future of accounting education. The CPA Journal; New York‚ 71(3)‚ 16-23. Almer‚ E. D.‚ Jones‚ K.‚ & Moeckel‚ C. L. (1998). The impact of one-minute papers on learning
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